Liverpool currently sit in second position on goal difference in the Premier League table, having gained maximum points from their opening five league fixtures.
Klopp's side edged past Paris Saint-Germain in their Champions League group C clash at Anfield on Tuesday and the manager will be hoping they can continue their winning run.
Speaking in the match programme ahead of today's fixture, Klopp urged his side to remain focused at the task in hand as he warned against complacency against Mark Hughes' side.
“Last Tuesday night was a tremendous feeling for everyone associated with Liverpool,” Klopp said. “But as is always the case we must immediately re-focus and all our efforts and energies have to go into this huge fixture today.
“There is really no need to give this message to players or supporters, as they will know it already, but this match is our most important of the season, because it is what’s next and therefore it is the only thing to say in this moment.
“I could not care for one second how many we have won in a row, or how healthy or otherwise our position is in any particular competition. To coin an English phrase I have learned: today is our be-all and end-all.
“It is not a case of ignoring what we experienced on Tuesday night – the opposite actually – but take from it what is useful.
“What is useful is that we saw that out-working your opponent is important – as it will be today. That being more hungry for the win is important – as it will be today. That outstanding atmosphere, feeling and passion from Anfield makes a difference – as it will do today.
“The lessons from Tuesday which are relevant for this and every game is that to win at this level, Champions League or Premier League, you must have the right mentality and attitude or you lose. It's that simple.
“Southampton will need no teamtalk for this match. They will see this as a fantastic opportunity. The positivity around us in this moment is fine, and of course I would sooner it be this way. But a positive feeling should not allow for a feeling of satisfaction.
“I have spoken many times about staying ‘angry’ in the competitive sense. Today it is critical. Southampton come here to ruin our day. They come to stop our momentum. They come to win at our home.
“They come to take the points. But we have a say in whether they achieve their aim. We have the chance to go again and repeat the intensity of Tuesday.”